Example of time domain and frequency domain

If you were to draw a graph of the voltage impinging on the speaker coils on
your stereo system over time, that would be a time series, which is a member ofthe time domain.

If you were to observe the lights dancing up and down on the front of your
equalizer while the music is playing, you would be observing the sameinformation presented in the frequency domain. Typically the lights on the left
represent low frequencies or bass while the lights on the right side representhigh frequencies or treble. Often there is a slider associated with each
vertical group of lights that allows you to apply filters to emphasize certainparts of the frequency spectrum and to de-emphasize other parts of the frequency
spectrum.

Forward and inverse transforms

There are two very similar forms of the Fourier transform. The forward
transform is typically used to transform information from the time domain intothe frequency domain. The inverse transform is typically used to transform
information from the frequency domain back into the time domain.

Sampled time series

The theoretical Fourier transform is defined using integral calculus as
applied to continuous functions. As a practical matter, in the digital world, wealmost never deal with continuous functions. Rather, we deal with functions that
have been reduced to a series of discrete numbers (or samples), which are theresult of some discrete measurement system.

(As mentioned earlier, recording the temperature in your office once
each minute for twenty-four hours would produce such a discrete series ofnumbers.)

Integration and summation

In many cases, the integration operation encountered in integral calculus can
be
approximated in the digital world by a summation operation using
discrete data. That is the case with the Fourier transform. Thus, the
(simple) summation form of the Fourier transform that is applied to a
discrete time series is known as the
Discrete Fourier Transform ,
or
DFT .

The FFT algorithms

The DFT is a computationally intense operation. Given certain restrictions
involving the number of values in the time series and the number of frequenciesat which the spectral analysis will be performed, there is are special
algorithm that can result in computational economy in performing the transform.The algorithms that are used to realize that economy are commonly referred to as
Fast Fourier Transform or
FFT algorithms.

DFT versus FFT

The DFT is more general than the FFT, but the FFT is much faster than the
DFT. It is important to understand that these are simply two differentalgorithms for doing the same thing. Either can be used to produce the same
results
(but as mentioned earlier, the FFT is somewhat more restricted as to the
number of time-domain and frequency-domain samples) .

Because the DFT algorithm is somewhat easier to understand than the FFT
algorithm, and also more general, I will concentrate on the DFT algorithm to explain how and why theFourier transform accomplishes what it accomplishes.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?

fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.

Tarell

what is the actual application of fullerenes nowadays?

Damian

That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.

Tarell

Join the discussion...

what is the Synthesis, properties,and applications of carbon nano chemistry

Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.